1 MATHEMATICS EDUCATION IN LITHUANIA Eugenijus Stankus (Vilnius University) Albina Vilimiene (Education Development Centre) Tallinn,

2 Mathematics education has been changing and developing in Lithuania as everything else for the last almost twenty years of independence. The changes affected educational programmes, attitude towards the subject of mathematics itself, teaching methods etc. We review the evolution of teaching mathematics in Lithuanian secondary schools. We deal with changes of educational programmes for mathematics of primary, secondary and comprehensive levels, peculiarities of system of external estimation of pupils’ achievements in Lithuania and the textbooks of school are reviewed.

3 Chronology of programmes for Lithuanian Schools ( ) Year 1994 – Project of new general programme for Lithuanian Schools; Year 1997 – certified general programmes for Lithuanian Schools, 1-10 grades; Year 2002 – certified general programmes and the Standard of Education for Lithuanian Schools, grades; Year 2003 – certified general programmes and the Standard of Education for primary and comprehensive levels of Lithuanian Schools.

4 Challenges – rapid changes in social and economical life of countries' and increasing possibilities of educational innovations. Governmental Acts which influenced renewal of general educational programmes: Regulations of National education strategies (Seimas of Republic of Lithuania, 4 July 2003, Nr. IX– 1700); Recommendation of Europarliament and Council of competence of life-long learning (2006/962/EB);

5 National programme for years of harmonious Education development. (Decision of Government of Republic of Lithuania, 2 October 2007, Nr. 1062). Data of International and National research of Achievement of students –TIMSS, PIRLS, PISA, CIVIC ( ); International experience (e.g. Finland, UK, Canada, Australian, New Zealand, Poland and etc.); Proposals of gymnasium teachers, of Universities teachers, of NGO, of politicians and other social partners.

6 Educational programmes are created, updated and implemented in Lithuania following these guidelines for the education content: make the content of education develop general and essential skills with special attention to training learning ability; deepen the individualization of learning regarding different needs of pupils; strengthen the attainability of the education content seeking the pupils to understand and apply with creativity what they learn; balance the extent of the content of subjects excluding the elements of the content that lost their relevance and including new, relevant elements.

7 Educational programmes for mathematics are influenced by the evolution of Lithuanian society (it’s political, economical, social, cultural and technological aspects), achievements of pupils as reflected in the international and national statistics, and the needs of higher education institutions, pedagogic community and parents. Regarding these regulations, general educational programmes for primary and comprehensive levels have been designed; they were approved by the Minister of Education and Science of Lithuania on August 26, 2008, and are now being actualized step by step. Year 2008 – Educational programme for primary and comprehensive levels (1-10 grades) These programmes will be put into effect from September 1, 2009, for the grades 1, 3, 5, 7 and 9 of all Lithuanian primary and secondary education schools.

8 Knowledge Attitude Ability

9 Knowledge. Mathematical facts obtained by students which could be applied in various fields of mathematics and life. Ability. Ability to learn mathematics and use mathematical concepts and relations for simple practical problems and in communication and collaboration. Attitude. Understanding of historical development, influence on modern science, practical importance and adaptability of mathematics. Competence is ability to succeed in achieving the goal in some field which is based on knowledge, understanding, abilities and attitude.

10 Mathematical Competence Areas of activities 8. Knowledge and understanding 9. Math. communi- cation 10. Math. thinking 11. Problem solving 12. Ability to learn and interest in Math. 1.Numbers and calculations 2. Expressions, equations, inequalities, systems 3. Relations and functions 4. Geometry 5. Measures and measurement 6. Statistics 7. Probability Theory

11 The General Education Plan, confirmed by the Minister of Education and Science, is released once in one or two years. It defines national standard for minimal weekly number of lessons. Schools are allowed to increase that number.

12 Grade School year B 12 A P P Number of weekly lessons P- specialised learning, A - extended level, B- comprehensive level.

13 Currently the project of General educational programmes for secondary level is being prepared. The project proposes two elective courses: the general course of mathematics and the extended course of mathematics (for all Lithuanian schools that follow the compulsory education programme). Two Lithuanian gymnasia (Vilnius Lyceum and Šiauliai Didždvaris gymnasium) offer studying mathematics as a part of the International Baccalaureate diploma programme. The programme for grades will constrict previous mathematical content. The probability theory course is intended to be constricted to only independent events. Integration will be taught only by examples for elementary functions. However, a new topic – basics of logic – will be included and is welcomed by the IT teachers.

14 We also consider the instruments for teaching and learning mathematics – textbooks. The school textbooks of mathematics are expected to reflect the whole content of the general programmes, allow to differentiate and individualize the learning process, be modern etc. Majority of contemporary mathematical school textbooks include a set of material, e.g. student’s textbook, teacher’s book, exercise-book, computer program. Manuscripts of textbooks are evaluated according to the official general criteria. Below we see these criteria and the number of alternative mathematical textbooks for each grade.

15 Textbook evaluation accuracy of content; accuracy of concepts, theories, interpretations; validity of content; tolerance; conformity to programmes and standards; possibility to differentiate learning; validity of pedagogic system; possibility to use textbook on one’s own; diversity of visual material; the style of language; orientation to practical experience and the context of life; conformity to other textbooks in the field; design, quality of printing.

16 There are two publishing houses in Lithuania which publish mathematical school textbooks. The textbook (often in a form of a manuscript) is evaluated by the Expert Commission and with it’s approval textbooks are marked by the certification “Recommended by the Ministry of Education and Science of the Republic of Lithuania”. Today students and teachers can by common agreement choose a textbook from the valid list of textbooks.

17 GradeNumber of alternative books Notes Translated from German* 621- * – A 2 – B

18 Achievements of learning mathematics in Lithuanian schools are estimated in two ways: by external estimation (school exam, state exam) and by national research (for grades 4, 6, 8, 10) and international research (PISA, TIMSS, PIRLS). External estimation and research External estimation of Mathematics achievements Researh of Mathematics achievements Examination of achievements of comprehensive level ( optional after grade 10 ) NEC Na tional researh (grades 4, 6, 8, 10), EDC International researh PISA, TIMSS, PIRLS NEC Maturity exam ( optional after grade 12 ) (school exam, state exam) NEC

Admitted to exam Did not come Number of confirmed works Participation in the National mathematics exam in

20 Characteristics of the task of the National maturity exam Total number of points Min. for passing the exam Failed the exam (in %) 9,817,713,820,213,516,67,58,0